Related papers: Markov evolutions and hierarchical equations in th…
We study the positive recurrence of multi-dimensional birth-and-death processes describing the evolution of a large class of stochastic systems, a typical example being the randomly varying number of flow-level transfers in a…
We here study random evolutions on Banach spaces, driven by a class of semi-Markov processes. The expectation (in the sense of Bochner) of such evolutions is shown to solve some abstract Cauchy problems. Further, the abstract telegraph…
We study one-parameter expanding evolution families of simply connected domains in the complex plane described by infinite systems of evolution parameters. These evolution parameters in some cases admit Hamiltonian formulation and lead to…
We construct a correlation functions evolution corresponding to the Glauber dynamics in continuum. Existence of the corresponding strongly continuous contraction semigroup in a proper Banach space is shown. Additionally we prove the…
We derive multicomponent relativistic second-order dissipative fluid dynamics from the Boltzmann equations for a reactive mixture of $N_{\text{spec}}$ particle species with $N_q$ intrinsic quantum numbers (e.g. electric charge, baryon…
The model of a multi-level system interacting with several reservoirs is considered. The exact reduced density matrix evolution could be obtained for this model without Markov approximation. Namely, this evolution is fully defined by the…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
We characterize a class of Markovian dynamics using the concept of divisible dynamical map. Moreover we provide a family of criteria which can distinguish Markovian and non-Markovian dynamics. These Markovianity criteria are based on a…
Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly…
We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual…
We construct the time evolution of Kawasaki dynamics for a spatial infinite particle system in terms of generating functionals. This is carried out by an Ovsjannikov-type result in a scale of Banach spaces, which leads to a local (in time)…
In the paper we discuss possible approaches to the problem of the rigorous derivation of quantum kinetic equations from underlying many-particle dynamics. For the description of a many-particle evolution we construct solutions of the Cauchy…
We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full…
We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…
We study the evolution of the universe which contains a multiple number of non-relativistic scalar fields decaying into both radiation and pressureless matter. We present a powerful analytic formalism to calculate the matter and radiation…
In this paper we examine a mutual control problem for systems of two abstract evolution equations subject to a proportionality final condition. Related observability and semi-observability problems are discussed. The analysis employs a…
We study existence, uniqueness, and a limiting behaviour of solutions to an abstract linear evolution equation in a scale of Banach spaces. The generator of the equation is a perturbation of the operator which satisfies the classical…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
We develop a rigorous formalism for the description of the kinetic evolution of many-particle systems with the dissipative interaction. The relationships of the evolution of a hard sphere system with inelastic collisions described within…
Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behaviour and for its possible application in near-term quantum technologies. However, understanding these…